Long-Term Evolution of Vacancies in Large-Area Graphene

Devices based on two-dimensional (2D) materials such as graphene and molybdenum disulfide have shown extraordinary potential in physics, nanotechnology, and electronics. The performances of these applications are heavily affected by defects in utilized materials. Although great efforts have been spent in studying the formation and property of various defects in 2D materials, the long-term evolution of vacancies is still unclear. Here, using a designed program based on the kinetic Monte Carlo method, we systematically investigate the vacancy evolution in monolayer graphene on a long-time and large spatial scale, focusing on the variation of the distribution of different vacancy types. In most cases, the vacancy distribution remains nearly unchanged during the whole evolution, and most of the evolution events are vacancy migrations with a few being coalescences, while it is extremely difficult for multiple vacancies to dissolve. The probabilities of different categories of vacancy evolutions are determined by their reaction rates, which, in turn, depend on corresponding energy barriers. We further study the influences of different factors such as the energy barrier for vacancy migration, coalescence, and dissociation on the evolution, and the coalescence energy barrier is found to be dominant. These findings indicate that vacancies (also subnanopores) in graphene are thermodynamically stable for a long period of time, conducive to subsequent characterizations or applications. Besides, this work provides hints to tune the ultimate vacancy distribution by changing related factors and suggests ways to study the evolution of other defects in various 2D materials.